Question

Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.

Answer 1

$$\begin{gathered} \text{Total possible outcomes}{=}^{20}{C}_3 \\ \text{Consecutive numbers chosen}=(1,2,3),(2,3,4)...(18,19,20) \\ \text{So, there are 18 favouable cases.} \\ P\left(A\right)=\frac{18}{{C^{20}}_3} \end{gathered}$$